1
FRE 6083 – Quantitative Methods in Finance - Copyright F. Novomestky 2007
Lecture 3 – Univariate and Bivariate
Probability
Agenda
É
Simulation of Exponential Random Variable
É
Simulation of Uniform Random Variable
É
Simulation of Gumbel Random Variable
É
Non-Parametric Density Models
É
Bivariate Continuous Distributions
É
Multivariate Continuous Distributions
É
Bivariate Discrete Distributions
É
Multivariate Discrete Distributions
2
FRE 6083 – Quantitative Methods in Finance - Copyright F. Novomestky 2007
Simulation of Exponential Random Variable
We use the inversion of CDF transformation from
Lecture 2 to generate sample random variables or
deviates that are independent and identically
distributed (i.i.d.) according the following
exponential distribution
(
)
(
)
(
)
1
exp
X
F
x
x
H
x
λ
⎡
⎤
=
−
−
⎣
⎦
We define the following relationship
(
)
1
X
X
F
U
−
=
3
FRE 6083 – Quantitative Methods in Finance - Copyright F. Novomestky 2007
Simulation of Exponential Random Variable
(
)
(
)
(
)
(
)
1
1
exp
exp
1
log 1
log 1
U
X
X
U
X
U
X
U
λ
λ
λ
λ
−
=
−
−
−
=
−
−
=
−
= −
−
Excel workbook file Class03a.xls contains the
sample simulation.
R workspace contains the
corresponding simulation using R.
Let’s estimate
the mean and variance of an exponential random
variable.
This
preview
has intentionally blurred sections.
Sign up to view the full version.
